Single Valued Neutrosophic VIKOR and Its Application to Wastewater Treatment Selection

Abstract

The fuzzy VIsekriterijumska optimizacija i KOmpromisno Resenje (VIKOR) has been used
in solving various multi-criteria decision-making problems where triangular fuzzy numbers are
utilized in defining decision-makers’ linguistic judgements. Most of the fuzzy VIKOR are built from
linguistic variables based on fuzzy sets and its generalization such as intuitionistic fuzzy sets.
Recent literature suggests that single-valued neutrosophic sets (SVNSs) can offer a better alternative
particularly when fuzzy sets have some extent of limitations in handling indeterminacy and
uncertainty. This paper proposes the SVNS-VIKOR where single-valued neutrosophic numbers are
utilized in defining linguistic variables of VIKOR. Differently from the typical fuzzy VIKOR which
directly utilizes fuzzy numbers with a single membership, the proposed method introduces three
independent memberships of truth, indeterminacy and false to enhance judgments in the group
decision-making environment. The obtained solutions would help policy makers in identifying the
best solution that could enhance the efficiency of treating wastewater.